Directional Coupling of Emitters into Waveguides: A Symmetry Perspective

Abstract

Recent experiments demonstrate strongly directional coupling of light into waveguide modes. Here, the symmetry mechanisms behind this effect are studied, and it is shown that the analysis of the symmetries and symmetry‐breakings of the emitter‐waveguide system allows to qualitatively understand directional coupling in several situations. The authors consider emitters either centered in a median plane of the waveguide, or displaced from it, and whose emissions have a well‐defined angular momentum in either one of the two different axis typically chosen experimentally, which are called transverse and vertical. These insights are matched by simulations, and previous experimental measurements. It is shown that handedness plays a secondary role in directional coupling. The spin‐momentum locking concept is generalized to an exponentially strong locking between the transverse angular momentum and the preferential coupling direction. A new selection rule is obtained that controls the coupling of electric(magnetic) multipolar emissions into waveguide modes. An experiment is proposed featuring a transverse magnetic bias that aggregates the directional emissions from many quantum dots on top of waveguides, in contrast to the typically used vertical bias, which effectively restricts experiments to using a single quantum dot. Finally, the Huygens' dipole is analyzed and the symmetries that enable its directional behavior revealed.

The optical helicity in a more algebraic approach to electromagnetism

“…3 [4]): Translational symmetry in focusing, and electromagnetic duality symmetry (see below) in scattering. For the directional coupling of emitters onto waveguides, it is readily shown that the polarization handedness of the emission cannot be responsible for the directionality, which is controlled by angular momentum [5], see Fig. 3.…”

“…for a real angle θ, and its action on the helical fields F λ (r,t) → F θ λ (r,t) = F λ (r,t) exp(-λiθ) (5) reveals that, in the same way that rotations are generated by angular momentum operators, e.g. R z (θ) = exp(-iθJ z ), duality is generated by the helicity operator D θ = exp(-iθΛ).…”

“…In each panel, the origin of coordinates is at the position of the emitter, and the coordinate axes are oriented as shown in the central part of the figure.The transformation properties of helicity allow us to conclude that it cannot be responsible for the directional coupling: For example, e) and h) show the same helicity producing the opposite directionality. Such contradictions do not arise for angular momentum, which is indeed the property of light which controls directionality[5].…”

Toggling Near‐Field Directionality via Polarization Control of Surface Waves

“…[ 3,15–19 ] In general, it is achieved through the judicious design of either asymmetric waveguide structures [ 20–22 ] or complex excitation sources, [ 7,23–28 ] such as the extensively studied circularly polarized dipoles. Circular electric (magnetic) dipoles [ 5,25,29–31 ] are featured with a spinning electric (magnetic) dipole moment. Correspondingly, their near‐field directionality is determined by the spin‐momentum locking and can be understood from the perspective of quantum spin Hall effect of light.…”